It is well known in the prior art that the inertial forces due to reciprocating and rotating masses in reciprocating engines can be minimized or cancelled by an appropriate counterbalance arrangement. Broadly, such prior arrangements for attempting to obtain complete engine balance have included the provision of additional balance weights disposed at opposite ends of the crankshaft which rotate at the same speed as the crankshaft but in the opposite direction. These balance weights have often been disposed on separate, additional, rotating shafts as shown, for example, in U.S. Pat. No. 4,414,934. In U.S. Pat. No. 3,415,237 the balance weights are provided at opposite ends of the crankshaft itself and concentric with the crankshaft. This avoids the requirement for additional, separate, rotating shafts but at the expense of requiring complex and expensive drive gearing. Various attempts have also been made to reduce the space required in the engine to achieve such balancing by rotatably mounting the balance weights on other already existing rotating shafts, such as on the camshaft of an internal combustion engine as shown in U.S. Pat. No. 3,203,274. It has also been known to use one or more of the additional rotating balancing shafts for driving auxiliary equipment, such as an oil pump. Further, in U.S. Pat. No. 3,759,238 there is shown a specific balancing arrangement of the foregoing described type for a single cylinder engine wherein the balance weights are rotatably mounted on extensions of dowell pins which are provided in the engine to achieve registry of the two sections of the housing/crankcase of a two-cycle type of internal combustion engine.
For example, reciprocating piston machines such as piston driven internal combustion engines, compressors and the like contain masses which are constrained to move in a reciprocating manner generally perpendicular to a rotating component known as a crankshaft. In order to balance the forces generated by the reciprocating masses, eccentric masses are located on the rotating elements such as the crankshaft. However, a reciprocating force as shown in FIG. 1A of the drawings, which is spatially fixed but has variable amplitude, can also be represented by the summation of two counter-rotating, fixed amplitude forces of half the peak amplitude of the reciprocating force as shown in FIG. 1B of the drawings. It follows from this analysis that the eccentric masses normally used on a rotating crankshaft component for balancing the crankshaft generate fixed-amplitude, rotating forces, and therefore can balance only half of the initial reciprocating imbalance, leaving a counter-rotating, fixed-amplitude, force.
The above analysis is depicted in FIGS. 1A and 1B wherein in FIG. 1A the generation of reciprocating forces by connection of a piston and crankshaft is illustrated together with the identification of the important parameters of this reciprocating system. The imbalance force produced by this system is given by the expression: EQU F.sub.y =mr.omega..sup.2 sin .theta. (1)
Where m equals the mass of the reciprocating piston, r is the radious of the throw arm of the crankshaft and .omega. is the angular speed of rotation of the crankshaft, t equals time, and .theta. equals .omega.t. FIG. 1B illustrates how the spatially fixed, variable-amplitude, imbalance force, Fy can be equivalently expressed as two counter-rotating, fixed-amplitude forces, F.sub.R +F.sub.R - each of whose values are given by the expressions: ##EQU1## If the resultant fixed amplitude counter-rotating forces are vectorially added, it will be seen that the vector addition along the x axis always equals 0. However, it will be noted that the vectorial components along the y (or vertical axis) do not sum to zero since F.sub.y R+=R.sub.R +sin .omega.t and F.sub.y R-=F.sub.R sin .omega.t which sum to F.sub.y =mr.omega..sup.2 sin .omega.t. This is the algebraic expression for the basic imbalance force present in a reciprocating piston system before an attempt of balancing in a conventional, normal manner by attaching an eccentric weight to the crankshaft of the machine 180.degree. out-of-phase with the piston mass, which weight cancels one-half the imbalance, specifically F.sub.R +.
To eliminate the remaining imbalance defined in the expression set forth above, a second rotating component has been added by providing a second parallel shaft connected to the first rotating shaft so as to assure a fixed phase relationship between the two rotating systems and to cause them to rotate in opposite direction. Eccentric balancing masses can then be added to the additional shaft to balance the residual counter-rotating imbalance of the crankshaft. Such arrangement is illustrated by the vector diagram shown in FIGS. 2A through 2D. FIG. 2A illustrates the nature of the reciprocating unbalance force F.sub.y discussed in the preceding paragraph. As noted above, this reciprocating imbalance force can be resolved into two fixed amplitude counter-rotating forces F.sub.R - and F.sub.R + as shown in FIG. 2B of the drawings. It is the usual practice in the industry to balance out one of these components by an eccentric weight secured to the rotating crankshaft. The size (mass) and phase relation of such a balancing weight is illustrated by the vector quantity F.sub.B + in FIG. 2C. It will be appreciated from FIG. 2C that the vector quantity F.sub.B + will exactly cancel out the rotating component F.sub.R + but leaves a remaining imbalance force F.sub.R -. In the past, efforts to balance out the remaining imbalance force represented by the vector component F.sub.R - in FIG. 2C and in FIG. 2D have resulted in the addition of a second shaft spaced from the first shaft a distance x.sub.s and rotated in a direction counter to the direction of rotation of the crankshaft. Fixed to the additional shaft is an eccentric mass represented by the vector quantity F.sub.B - which it is noticed will rotate to exactly balance out the imbalance force F.sub.R -. This approach can be seen to provide a total balancing of the reciprocating imbalance forces, but because of the offset distance (x.sub.s in FIG. 2D) between the two shafts and therefore the centers of force rotation, a moment is induced. This moment is in a form of reciprocating torque (T=F.sub.B -(x.sub.s)) about an axis parallel to the shafts. This reciprocating torque is referred to as a "rocking couple." To minimize this rocking couple effect, the distance x.sub.s must be minimized. Alternatively, at extra cost and space, a second extra shaft may be added on the other side of the main shaft to share the balancing duty by splitting the balancing force F.sub.B - into two equal forces rotating in the same direction but disposed from the main shaft to be balanced by a distance x.sub.s and on the opposite side of the shaft another distance -x.sub.s from the main shaft. With such a two balancing shaft arrangement, the net residual torque is given by the expression: ##EQU2##
The effect of the two balancing shaft technique is to put the line of action of the balancing force into the same location as the line of action of the original imbalance and to simulate concentric counter-rotating shafts in a manner disclosed in U.S. Pat. No. 3,415,237 issued Dec. 10, 1968, to J. R. Harkness for an "An Internal Combustion Engine Imbalancing Means Therefore."